They make an important methodological point - one that applies to a lot of work on minimum legal drinking ages. It is really easy to set up a regression discontinuity design using the birthday as the point of the discontinuity. The 17 year old, before the birthday, is the same person a week later, except with access to alcohol. Sure. But the RDD method can't tell you whether you've identified a birthday effect that will wash out over time, or a persistent negative effect resulting from a change in access to alcohol.

New Zealand makes for a good case study because the change in the minimum legal alcohol purchase age is relatively recent. So we can check what happens around birthdays before and after the change, set appropriate counterfactual trends, and look at overall effects on accident rates for those in the age group that switches status.

They conclude:

Overall, we find no evidence that changing the drinking age from 20 to 18 led to more
vehicular accidents or alcohol-related accidents among teens. This is true both in the short-run
following the law change and when examining cumulative accidents for the affected cohorts.
We find that accidents do increase after one’s 18th birthday, but this appears to be a short-run
phenomenon. Finally, our parametric regression models suggest that reducing the drinking age
led to a decline in risky driving by youth who were already 15 at the time of the law change
but had no longer-run impacts on youth risky driving among younger cohorts. We speculate
that this occurred because of the extensive public discussion about the drinking age change
that took place and because teens are likely to be particularly focused on the near future. We
also present supportive evidence from infrequent health surveys showing a similar pattern for
alcohol consumption among different youth cohorts. Our results support the argument that the
legal drinking age can be lowered without leading to increases in detrimental outcomes for
youth and call into question previous studies that have made policy recommendations by
extrapolating from results identified using age-based RDDs.

Overall, our results support the argument being made by groups like Amethyst Initiative and
Choose Responsibility (see http://www.chooseresponsibility.org/proposal/) that the legal
drinking age can be lowered without leading to detrimental outcomes for youth. The current age limit of 21 in the US is higher than in Canada, Mexico and most western European
countries. The arguments against lowering the drinking age typically include the idea that,
even if a new steady-state with a lower drinking age might be beneficial, the transition to that
new steady-state might be very costly. The evidence in our paper from a country with drinking
habits very similar to the US suggests that this does not have to be the case.